Alright lets get started by discussing random variables. As you all know, the occurrence of events out in the world, whether it be us staying remote for the whole quarter or me TAing this class well, have a degree of uncertainty. If they didn’t, then we wouldn’t even need statistics which we use to quantify that uncertainty.
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We call these occurrences random variables, because they are variables that take on specific values with specific probabilities.
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More formally, random variables are measurable functions that map outcomes of a stochastic process to a measurable space.
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Typically they are denoted by a capital letter.
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For instance, we can denote the outcome of a fair coin flip as this capital Y, and map it to a measurable space of 1 and 0 if the coin lands heads or tails. The probability of either outcome occurring is 0.5.